Symmetry in Physics, Spontaneous Symmetry Breaking

Spontaneous Symmetry Breaking (in physics)

For spontaneous symmetry breaking to occur,
there must be a system that is symmetric with respect to certain equally likely outcomes.
However, if the system is sampled (actually used or interacted with in any way), a specific outcome must occur.

Though the system as a whole is symmetric,

it is never encountered with this symmetry, but only in one specific asymmetric state.

We say: There is a hidden symmetry spontaneously broken in that theory.

Perhaps the best way to explain how symmetry breaking works is to give a few examples:

Let us first consider a dinner arrangement in which a number of people are seated around a circular table with water glasses placed between them.
Which one should someone use, the one to his right, or the one to his left?

Good manners say the one on the right, but aside of arbitrary rules of etiquette, left and right serve equally well.

However, as soon as someone chooses a glass, the symmetry is broken.
The impetus to choose is not part of the system: It would be another factor (thirst).

Nonetheless, if one person spontaneously drank from the glass on their left, so would that person's neighbor, and in the end everyone would have used the glass on the left.

We see: The symmetry exists until the moment someone picks up a glass. At that moment the left-right symmetry is spontaneously broken.

It is important to note that no law of physics dictates that the first person choosing has to choose left or right.
But as soon as one alternative was chosen, there is no longer symmetry in the system.

A symmetry, by the way, can appear to be preserved when viewed on one distance scale even though it appears to be broken on another. Here is an example:

Assume a very long wall looking the same everywhere because you are close enough so that its bounderies are out of your field of vision (a symmetric view).
Standing back however, you might see that the wall's left end is nearer than the wall's right end (no longer a symmetric view).

Almost any symmetry you care to name is not preserved in our world. For example, there are many sym­metries that would be present in empty space, such as rotational or translational invariance,
which tell us that all directions and positions are equivalent.

But space is not empty: It is punctuated by stars and planets which occupy particular positions and are so deforming the fabric of spacetime.
You see: This is breaking spacetime's symmetry though it remains imp­licit in the physical laws describing spacetime.